# [SOLVED]eigenvalue and eigenfunction for Fredholm method

#### dwsmith

##### Well-known member
Given
$f(x) = \lambda\int_0^1xy^2f(y)dy$
At order $$\lambda^2$$ and $$\lambda^3$$, we have repeated zeros so
$D(\lambda) = 1 - \frac{\lambda}{4}.$
Then we have
$\mathcal{D}(x, y;\lambda) = xy^2$
so
$f(x) = \frac{\lambda}{D(\lambda)}\int_0^1\mathcal{D}(x, y;\lambda)dy.$
How do I get the eigenfunction and value from this method?